Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 8

Speedup: 1.0×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

Python

def code(x, y, z):
	return x + ((y - x) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

Python

def code(x, y, z):
	return x + ((y - x) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) z x))

C

double code(double x, double y, double z) {
	return fma((y - x), z, x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), z, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * z + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \left(y - x\right) \cdot z \]
2. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot z + x} \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z, x\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y - x, z, x\right) \]

Alternative 2: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-130} \lor \neg \left(x \leq 2.9 \cdot 10^{-101}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.4e-130) (not (<= x 2.9e-101))) (* x (- 1.0 z)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.4e-130) || !(x <= 2.9e-101)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6.4d-130)) .or. (.not. (x <= 2.9d-101))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.4e-130) || !(x <= 2.9e-101)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.4e-130) or not (x <= 2.9e-101):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.4e-130) || !(x <= 2.9e-101))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.4e-130) || ~((x <= 2.9e-101)))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.4e-130], N[Not[LessEqual[x, 2.9e-101]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.3999999999999999e-130 or 2.9e-101 < x

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in x around inf 80.3%

      \[\leadsto \color{blue}{\left(-1 \cdot z + 1\right) \cdot x} \]
   3. Step-by-step derivation

      1. distribute-rgt1-in 80.3%

         \[\leadsto \color{blue}{x + \left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 80.3%

         \[\leadsto x + \color{blue}{\left(-z\right)} \cdot x \]

      3. cancel-sign-sub-inv 80.3%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 80.3%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in x around 0 80.3%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   if -6.3999999999999999e-130 < x < 2.9e-101

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-130} \lor \neg \left(x \leq 2.9 \cdot 10^{-101}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-5} \lor \neg \left(z \leq 0.4\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e-5) (not (<= z 0.4))) (* (- y x) z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-5) || !(z <= 0.4)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.5d-5)) .or. (.not. (z <= 0.4d0))) then
        tmp = (y - x) * z
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-5) || !(z <= 0.4)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e-5) or not (z <= 0.4):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e-5) || !(z <= 0.4))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e-5) || ~((z <= 0.4)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e-5], N[Not[LessEqual[z, 0.4]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000012e-5 or 0.40000000000000002 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot z} \]

   if -2.50000000000000012e-5 < z < 0.40000000000000002

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in x around inf 78.1%

      \[\leadsto \color{blue}{\left(-1 \cdot z + 1\right) \cdot x} \]
   3. Step-by-step derivation

      1. distribute-rgt1-in 78.1%

         \[\leadsto \color{blue}{x + \left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 78.1%

         \[\leadsto x + \color{blue}{\left(-z\right)} \cdot x \]

      3. cancel-sign-sub-inv 78.1%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 78.1%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-5} \lor \neg \left(z \leq 0.4\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 4: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -90 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -90.0) (not (<= z 1.0))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -90.0) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-90.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y - x) * z
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -90.0) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -90.0) or not (z <= 1.0):
		tmp = (y - x) * z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -90.0) || !(z <= 1.0))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -90.0) || ~((z <= 1.0)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -90.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -90 or 1 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 98.9%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot z} \]

   if -90 < z < 1

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto x + \color{blue}{z \cdot \left(y - x\right)} \]

      2. sub-neg 99.9%

         \[\leadsto x + z \cdot \color{blue}{\left(y + \left(-x\right)\right)} \]

      3. distribute-lft-in 99.9%

         \[\leadsto x + \color{blue}{\left(z \cdot y + z \cdot \left(-x\right)\right)} \]

      4. fma-def 99.9%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(z, y, z \cdot \left(-x\right)\right)} \]

   3. Applied egg-rr 99.9%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(z, y, z \cdot \left(-x\right)\right)} \]

   4. Taylor expanded in y around inf 97.1%

      \[\leadsto x + \color{blue}{y \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 97.1%

         \[\leadsto x + \color{blue}{z \cdot y} \]

   6. Simplified 97.1%

      \[\leadsto x + \color{blue}{z \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -90 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.2e-5) (* y z) (if (<= z 6.3e-9) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e-5) {
		tmp = y * z;
	} else if (z <= 6.3e-9) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.2d-5)) then
        tmp = y * z
    else if (z <= 6.3d-9) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e-5) {
		tmp = y * z;
	} else if (z <= 6.3e-9) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.2e-5:
		tmp = y * z
	elif z <= 6.3e-9:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.2e-5)
		tmp = Float64(y * z);
	elseif (z <= 6.3e-9)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.2e-5)
		tmp = y * z;
	elseif (z <= 6.3e-9)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.2e-5], N[(y * z), $MachinePrecision], If[LessEqual[z, 6.3e-9], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e-5 or 6.3000000000000002e-9 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in x around 0 58.1%

      \[\leadsto \color{blue}{y \cdot z} \]

   if -2.1999999999999999e-5 < z < 6.3000000000000002e-9

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around 0 77.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* x (- z)) (if (<= z 5.8e-8) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * -z;
	} else if (z <= 5.8e-8) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = x * -z
    else if (z <= 5.8d-8) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * -z;
	} else if (z <= 5.8e-8) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * -z
	elif z <= 5.8e-8:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * Float64(-z));
	elseif (z <= 5.8e-8)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * -z;
	elseif (z <= 5.8e-8)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(x * (-z)), $MachinePrecision], If[LessEqual[z, 5.8e-8], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot z} \]

   3. Taylor expanded in y around 0 55.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 55.4%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-out 55.4%

         \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   5. Simplified 55.4%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   if -1 < z < 5.8000000000000003e-8

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in z around 0 76.5%

      \[\leadsto \color{blue}{x} \]

   if 5.8000000000000003e-8 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in x around 0 67.2%

      \[\leadsto \color{blue}{y \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * z);
}

Python

def code(x, y, z):
	return x + ((y - x) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \left(y - x\right) \cdot z \]

2. Final simplification 99.9%

   \[\leadsto x + \left(y - x\right) \cdot z \]

Alternative 8: 36.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

   \[x + \left(y - x\right) \cdot z \]

2. Taylor expanded in z around 0 41.7%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 41.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023174 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))